Optimizing an inventory of a supply chain

ABSTRACT

Optimizing inventory targets for nodes of a supply chain to satisfy a target customer service level may include accessing a supply chain model that has an assumed value for each of a number of inputs. An optimized inventory target is calculated according to the supply chain model to satisfy the target customer service level, and a measured actual customer service level and a measured actual value for each input are accessed. If the measured actual customer service level fails to satisfy the target customer service level, deviations between the measured actual and assumed values for each input are determined. An input for which the deviation is significant is identified to be a root cause of the failure. For a subsequent time period, using the deviation for the identified input as feedback, the assumed value for the identified input is adjusted, and a reoptimized inventory target is calculated to satisfy the target customer service level.

RELATED APPLICATIONS

[0001] This application claims benefit under 35 U.S.C. § 119(e) of U.S.Provisional Application Serial No. 60/470,068, entitled “StrategicInventory Optimization,” filed May 12, 2003, Attorney's Docket020431.1310.

TECHNICAL FIELD

[0002] This invention relates generally to the field of supply chainanalysis and more specifically to optimizing an inventory of a supplychain.

BACKGROUND

[0003] A supply chain supplies a product to a customer, and may includenodes that store inventory such as parts needed to produce the product.A known technique for maintaining a proper amount of inventory at eachnode may involve setting a reorder point at which inventory isreordered. For example, a node may reorder parts when its inventory isless than twenty units. Known techniques for maintaining a proper amountof inventory at each node, however, may require storage of excessinventory at the nodes and result in additional inventory carryingcosts. It is generally desirable to reduce excess inventory andassociated inventory carrying costs.

SUMMARY OF THE INVENTION

[0004] In accordance with the present invention, disadvantages andproblems associated with previous supply chain analysis techniques maybe reduced or eliminated.

[0005] According to one embodiment of the present invention, a method isprovided for optimizing inventory targets for nodes in a multi-echelonsupply chain to satisfy a target customer service level. A supply chainmodel is accessed comprising an assumed value for each of a number ofinputs for a first time period. Inputs may include: mean order leadtime; variability of order lead time; for each of a number of order leadtime intervals, mean demand within the order lead time interval; foreach of the number of order lead time intervals, variability of demandwithin the order lead time interval; mean supply lead time for each ofthe nodes; and variability of supply lead time for each of the nodes.For the first time period, according to the supply chain model includingthe assumed values for the inputs, an optimized inventory target iscalculated for each of the nodes to satisfy the target customer servicelevel. For the first time period, a measured actual customer servicelevel and a measured actual value for each of the inputs are accessed.If the measured actual customer service level for the first time perioddoes not satisfy the target customer service level, then for each of theinputs a deviation between the measured actual and assumed values forthe input is determined for the first time period, and at least one ofthe inputs for which the deviation for the first time period issignificant is identified to be a root cause of the measured actualcustomer service level for the first time period not satisfying thetarget customer service level. For a subsequent second time period,using the determined deviation for the identified input for the firsttime period is used as feedback, the assumed value for the identifiedinput in the supply chain model is adjusted, and a reoptimized inventorytarget is calculated for each of the nodes to satisfy the targetcustomer service level.

[0006] Certain embodiments of the invention may provide one or moretechnical advantages. For example, a technical advantage of oneembodiment may be that inputs to an optimization problem may beevaluated using feedback from the results of a previous optimizationprocedure. Evaluating the inputs may allow for more accurateoptimization results. As another example, the optimization process maybe repeated in an iterative closed-loop process that is consistent andrepeatable over successive time periods. Repeating the optimizationprocess may provide for increasing accuracy of the optimization results.

[0007] Certain embodiments of the invention may include none, some, orall of the above technical advantages. One or more other technicaladvantages may be readily apparent to one skilled in the art from thefigures, descriptions, and claims included herein.

BRIEF DESCRIPTION OF THE DRAWINGS

[0008] For a more complete understanding of the present invention andits features and advantages, reference is made to the followingdescription, taken in conjunction with the accompanying drawings, inwhich:

[0009]FIG. 1 is a block diagram illustrating an example system foroptimizing inventory in a supply chain;

[0010]FIG. 2 is a flowchart illustrating an example method foroptimizing inventory in a supply chain;

[0011]FIG. 3 illustrates an example matrix that may be used to generatecriticality groups;

[0012]FIG. 4 is a diagram illustrating an example supply chain thatreceives supplies from one or more suppliers and provides products toone or more customers;

[0013]FIG. 5 is a flowchart illustrating an example method for inventoryoptimization;

[0014]FIGS. 6A through 6C illustrate example order lead time profiles;

[0015]FIG. 7 is a bar graph illustrating example cycle times for nodesof a supply chain;

[0016]FIG. 8 is a table with example demand percentages;

[0017]FIG. 9 is a diagram illustrating redistributed demand for anexample supply chain;

[0018]FIG. 10 illustrates an example node for which an inventory may becalculated;

[0019]FIG. 11 illustrates an example supply chain that includes one nodesupplying another node;

[0020]FIG. 12 illustrates an example supply chain that includes one nodesupplying two nodes; and

[0021]FIG. 13 illustrates an example supply chain that includes twonodes supplying one node.

DESCRIPTION OF EXAMPLE EMBODIMENTS

[0022]FIG. 1 is a block diagram illustrating an example system 10 foroptimizing inventory in a supply chain that supplies products tocustomers in response to customer demand. For example, system 10 mayoptimize target safety stocks or other inventory measures, within aminimum overall target customer service level (CSL), at each node in thesupply chain for each item flowing through the supply chain. Accordingto one embodiment, system 10 may use assumptions to formulate a supplychain model, and evaluate the assumptions with respect to historicalperformance. According to another embodiment, products may be segmentedinto policy groups, such as criticality groups, for example, in order todetermine customer service levels for the products. According to yetanother embodiment, order lead times may be used to redistributecustomer demand to upstream nodes of the supply chain.

[0023] According to the illustrated embodiment, system 10 includes aclient system 20, a server system 24, and a database 26 coupled as shownin FIG. 1. Client system 20 allows a user to communicate with serversystem 24 to optimize inventory in a supply chain. Server system 24manages applications for optimizing inventory in a supply chain.Database 26 stores data that may be used by server system 24.

[0024] According to the illustrated embodiment, server system 24includes one or more processors 30 and one or more engines 32 coupled asshown in FIG. 1. Processors 30 manage the operation of server system 24,and may comprise any device operable to accept input, process the inputaccording to predefined rules, and produce an output. According to oneembodiment, processors 30 may comprise parallel processors in adistributed processing environment. Server system 24 may operate todecompose an optimization problem into a number of smaller problems tobe handled by a number of processors 30. As an example, server system 24may independently calculate the optimized inventory target for each of anumber of nodes using a different processor 30.

[0025] According to the illustrated embodiment, engines 32 includes ademand manager 33, a simulation engine 34, an analytics engine 36, anoptimization engine 38, and a supply chain planning engine 40. Engines32 may be configured in processors 30 in any suitable manner. As anexample, engines 32 may be located in different processors 30. Asanother example, a backup for an engine 32 and the engine 32 itself maybe located in different processors 30. Demand manager 33 provides demandforecasting, demand planning, other demand management functionality, orany combination of the preceding. Simulation engine 34 simulatesexecution of a supply chain. Simulation engine 34 may be used toevaluate supply chain models. Analytics engine 36 analyzes inventory,demand, and order lead time data. Analytics engine 36 may be used tosegment customers, items, locations, other entities, or any combinationof the preceding into policy groups for different purposes. Optimizationengine 38 optimizes the inventory at the nodes of a supply chain. Demandmay be distributed to upstream nodes according to a demand forecast, andoptimization engine 38 may optimize inventory for the distributeddemand. Supply chain planning engine 40 generates a plan for a supplychain.

[0026] Client system 20 and server system 24 may each operate on one ormore computers and may include appropriate input devices, outputdevices, mass storage media, processors, memory, or other components forreceiving, processing, storing, and communicating information accordingto the operation of system 10. For example, the present inventioncontemplates the functions of both client system 20 and server system 24being provided using a single computer system, such as a single personalcomputer. As used in this document, the term “computer” refers to anysuitable device operable to accept input, process the input according topredefined rules, and produce output, for example, a personal computer,work station, network computer, wireless telephone, personal digitalassistant, one or more microprocessors within these or other devices, orany other suitable processing device.

[0027] Client system 20, server system 24, and database 26 may beintegrated or separated according to particular needs. If anycombination of client system 20, server system 24, or database 26 areseparated, they may be coupled to each other using a local area network(LAN), a metropolitan area network (MAN), a wide area network (WAN), aglobal computer network such as the Internet, or any other appropriatewire line, optical, wireless, or other link.

[0028] Modifications, additions, or omissions may be made to system 10without departing from the scope of the invention. For example, system10 may have more, fewer, or other modules. Moreover, the operations ofsystem 10 may be performed by more, fewer, or other modules. Forexample, the operations of simulation engine 34 and optimization engine38 may be performed by one module, or the operations of optimizationengine 38 may be performed by more than one module. Additionally,functions may be performed using any suitable logic comprising software,hardware, other logic, or any suitable combination of the preceding. Asused in this document, “each” refers to each member of a set or eachmember of a subset of a set.

[0029]FIG. 2 is a flowchart illustrating an example method foroptimizing inventory in a supply chain. The method may be used toseparate the demand analysis from the supply analysis by redistributingthe demand to upstream nodes and then calculating the inventory requiredto satisfy the redistributed demand. Separating the demand may providefor more efficient inventory analysis. The method begins at step 48,where a supply chain model is formulated for a supply chain. A supplychain model may be used to simulate the flow of items through the supplychain, and may represent one or more constraints of a supply chain. Aconstraint comprises a restriction of the supply chain. The supply chainmodel may have one or more assumptions. An assumption comprises anestimate of one or more parameters of a supply chain model.

[0030] The assumptions are evaluated at step 50. The assumptions may beevaluated by simulating the supply chain using the supply chain modeland validating the simulation against historical data describing actualperformance of the supply chain. Historical data describing a first timeperiod may be applied to the supply chain model to generate a predictiondescribing a second time period. For example, given one year of data,the first ten months of data may be used with the supply chain model topredict the last two months of data. The prediction for the second timeperiod may be compared to the historical data describing the second timeperiod in order to evaluate the assumptions of the supply chain model.The assumptions may be adjusted in response to the evaluation.

[0031] The inventory is analyzed at step 52. The inventory may beanalyzed by segmenting products into policy groups such as criticalitygroups. Each criticality group may correspond to a particular inventorypolicy such as a customer service level. Customer demand and order leadtime may also be analyzed to determine demand and order lead time meansand variability. The inventory is optimized at step 54 to determine anoptimized inventory for each node of the supply chain. The sensitivityof the optimized inventory may be analyzed by adjusting the assumptionsand checking the sensitivity of the inventory to the adjustment.According to one embodiment, the assumptions may be relaxed in order toreduce the complexity of the optimization.

[0032] The optimization may be validated at step 56. During validation,any assumptions that were relaxed during optimization may be tightened.An inventory policy may be determined at step 58. According to oneembodiment, a user may decide upon an inventory policy in response tothe validation results. The inventory policy is implemented in thephysical supply chain at step 60.

[0033] The inventory performance may be evaluated at step 62 bydetermining whether the inventory performance satisfies inventoryperformance measures. In response to evaluating the inventoryperformance, the method may return to step 48 to formulate anothersupply chain model, to step 50 to re-evaluate the assumptions, to step52 to re-analyze the inventory, or to step 58 to determine anotherinventory policy, or the method may terminate. According to oneembodiment, an actual customer service level may be measured at a firsttime period. If the actual customer service level fails to satisfy thetarget customer service level, deviations between actual and assumedinput values may be determined. The deviations may be determinedaccording to defined workflows that are consistent and repeatable oversuccessive time periods. An input value with a deviation may beidentified to be a root cause of the failure and this information usedas feedback for a subsequent time period. During the subsequent timeperiod, the assumed value for the identified input may be adjusted andused to calculate a reoptimized inventory target. According to theembodiment, the steps of the method may be repeated in an iterativeclosed-loop process that is consistent and repeatable over successivetime periods. The iterative closed-loop process may use the assumedvalues of the inputs as its inputs and the actual customer service levelas its output.

[0034] Modifications, additions, or omissions may be made to the methodwithout departing from the scope of the invention. For example, the stepof evaluating the assumptions may be omitted. Additionally, steps may beperformed in any suitable order without departing from the scope of theinvention. For example, the step of evaluating the assumptions may beperformed after the step of analyzing inventory. Furthermore, althoughthe method is described as optimizing inventory for each node of thesupply chain, the method may be used to optimize inventory for a subsetof one or more nodes of the supply chain.

[0035]FIG. 3 illustrates an example matrix M_(i . . . j) 66 that may beused to generate policy groups such as criticality groups. A policygroup comprises a set of entities strategically segmented for aparticular purpose. An entity may comprise, for example, a product, alocation, or a customer of a supply chain. According to one embodiment,a policy group may refer to a criticality group for which a servicelevel policy is defined. A service level policy describes the level ofservice for an entity, and may include a customer service level, a leadtime, or other parameter. As an example, segmentation may classifycustomers into criticality groups, where each criticality group has aspecified customer service level. Criticality groups may be used todefine different service levels for different customers. According toanother embodiment, a policy group may refer to a set of entities thatexhibit common buying behaviors, for example, common order lead timeprofiles.

[0036] According to the illustrated example, matrix M_(i . . . j) 66 isused to segment products into criticality groups, where each entry, orcell, m_(i . . . j) represents a criticality group with a specificservice level policy. Matrix M_(i . . . j) 66 may have any suitablenumber of indices i . . . j, where each index represents an attribute ofthe entities. An attribute comprises a feature of an entity that isrelevant to the service level associated with the entity, and may bequantitative or non-quantitative. Examples of quantitative attributesinclude inventory volume, revenue calculated as volume times price,margin volume calculated as price minus cost, or other attributes.Examples of non-quantitative attributes may include product tier or lifecycle, number of customers served, or other attributes. According to theillustrated example, index i represents the relative speed with whichitems for the product move through the supply chain, and j representswhether there is a hub agreement with the nodes through which the itemsflow. An index may, however, represent any suitable attribute. As anexample, an index may be used to define target customer service levels,minimum offered lead times, maximum offered lead times, or anycombination of the preceding for each criticality group. Eachcriticality group may represent a unique combination of item, location,and channel.

[0037] As used herein, the term “matrix” is meant to encompass anysuitable arrangement of attributes in which each attribute associatedwith the matrix corresponds to at least one index of the matrix and maycorrespond to any number of indexes of the matrix. Such a matrix mayhave any suitable format. As an example, different cells may havedifferent indices. As another example, policy groups corresponding todifferent cells may overlap. Membership to overlapping policy groups maybe resolved by, for example, assigning priorities to the policy groups.An attribute not corresponding to any index of the matrix may beassigned to a default policy group.

[0038]FIG. 4 is a diagram illustrating an example supply chain 70 thatreceives supplies from one or more suppliers 80 and provides products toone or more customers 84. Items flow through supply chain 70, and may betransformed or remain the same as they flow through supply chain 70.Items may comprise, for example, parts, supplies, or services that maybe used to generate the products. The products may include none, some,or all of some or all of the items. For example, an item may comprise apart of the product, or an item may comprise a supply that is used tomanufacture the product, but does not become a part of the product.Downstream refers to the direction from suppliers 80 to customers 84,and upstream refers to the direction from customers 84 to suppliers 80.

[0039] Supply chain 70 may include any suitable number of nodes 76 andany suitable number of arcs 78 configured in any suitable manner.According to the illustrated embodiment, supply chain 70 includes nodes76 and arcs 78. Items from supplier 80 flow to node 76 a, which sendsitems to node 76 b. Node 76 b sends items to node 76 c, which sendsitems to customer 84 a and nodes 76 d and 76 e. Nodes 76 d and 76 eprovide products to customers 84 b and 84 c, respectively.

[0040] Node 76 a may comprise one of one or more starting nodes 76 aupstream from one or more ending nodes 76 d-e. Starting nodes 76 a mayreceive items directly from supplier 80 or from an upstream node 76, andending nodes 76 c-e may send items directly to a customer 84 a-c or to adownstream node 76. A starting node 76 a and an ending node 76 c-e maydefine a path that includes starting node 76 a, ending node 76 c-e, andany intermediate nodes 76 b-c between starting node 76 a and an endingnode 76 c-e.

[0041] Although supply chain 70 is illustrated as having five nodes 76a-e and four arcs 78 a-d, modifications, additions, or omissions may bemade to supply chain 70 without departing from the scope of theinvention. For example, supply chain 70 may have more or fewer nodes 76or arcs 78. Moreover, nodes 76 or arcs 78 may have any suitableconfiguration. For example, node 76 a may supply items to node 76 c, butnot to node 76 b. As another example, any node 76 may supply itemsdirectly to a customer 84.

[0042] The products may be delivered to a customer 84 according to anorder lead time for customer 84. An order lead time represents the timeperiod during which supply chain 70 may satisfy an order. The order leadtime for customer 84 may be calculated as the time between the time whenthe order is finalized and the time when the order is to be provided tocustomer 84. The time when an order is finalized may be different fromthe time when the order was placed, since the order may be modifiedbefore the order is finalized. A finalized order may refer to an orderat any suitable stage of the supply chain process. For example,finalized orders may refer to last changed orders, orders that have beenshipped, orders that are in backlog, other suitable orders, or anycombination of the preceding.

[0043] The order lead time for customer 84 may be described using aprobability distribution for expected order lead time. A probabilitydistribution for expected order lead time describes the probabilitydistribution of demand relative to order lead time. A probabilitydistribution for expected order lead time may be calculated from anorder lead time profile. An order lead time profile describes demandwith respect to order lead time, and may be generated from a demandprofile that describes demand with respect to time. The demand may beexpressed as unit demand, as a proportion of the demand, or in any othersuitable manner. As an example, an order lead time profile may describea cumulative percentage of the demand with respect to order lead time.For example, an order lead time profile may have a y axis representingthe cumulative percentage of demand and an x axis representing orderlead time expressed as number of days. An example order lead timeprofiles is described in more detail with reference to FIG. 6.

[0044] Although the probability distribution for expected order leadtime may be calculated from an order lead time profile, the probabilitydistribution may be determined from other suitable types of informationusing any suitable number of parameters. For example, the probabilitydistribution may be determined from the absolute demand volume withrespect to time. As another example, the probability distribution may bedetermined using a fuzzy logic approach. A fuzzy logic approach may, forexample, designate that a certain amount or portion of the demand has aspecific order lead time.

[0045] All of the demand typically does not have the same order leadtime. For example, 70% of the demand may have an order lead time of lessthan 20 days, and 30% of the demand may have an order lead time of 20days or greater. If a node 76 can replenish its inventory in time tosatisfy a portion of the demand, node 76 does not need to stock theinventory for that portion of the demand. For example, if node 76 canreplenish its inventory in less than 20 days to satisfy 30% of thedemand, node 76 does not need to stock inventory for 30% of the demand.

[0046] According to one embodiment, the demand initiated by a customer84 may be redistributed from a downstream node 76 to one or moreupstream nodes 76. For example, the demand initiated by customer 84 a,84 b, or 84 c may be redistributed from downstream node 76 c, 76 d, or76 e, respectively, to one or more upstream nodes 76 a-c. Optimizationof the redistributed demand may be postponed to upstream nodes 76 a-c.Redistributing demand upstream may serve to optimize supply chain 70.Typically, maintaining items at upstream nodes 76 is less expensive thanmaintaining items at downstream nodes 76. Additionally, more developeditems at downstream nodes 76 are typically more susceptible to marketchanges. A method for optimizing inventory by redistributing demand toupstream nodes 76 is described in more detail with reference to FIG. 5.

[0047] According to one embodiment, redistributing the demand upstreaminvolves taking into account the time it takes for supplies needed atnodes 76 to be replenished and the reliability of the supply nodes 76.The replenishment time may be determined from supply lead times (SLTs).According to the illustrated example, the mean supply lead time(μ_(SLT)) for node 76 a is 20.0 days with a variability (σ_(SLT)) of 6.0days, the mean supply lead time for arc 78 a is 1.5 days with avariability of 0.5 days, the mean supply lead time for node 76 b is 6.0days with a variability of 2.67 days, the mean supply lead time for node76 c is 0.0 days with a variability of 0.00 days, the mean supply leadtime for arc 78 b is 1.0 day with a variability of 0.33 days, and themean supply lead time for arc 78 c is 1.5 days with a variability of 0.5days. Node 76 c may be considered a global distribution node. Thereliability of the supply nodes 76 may be determined from the customerservice levels of nodes 76. According to the illustrated example, thecustomer service level for node 76 a is 80%, and the customer servicelevels for nodes 76 b and 76 c are 96%.

[0048]FIG. 5 is a flowchart illustrating an example method for inventoryoptimization. The method begins at step 104, where order lead timeprofiles are created for different categories. Categories may be used toorganize customers, products, locations, other entity, or anycombination of the preceding. For example, customers 84 may becategorized according to features that affect the order lead times ofcustomers 84, such as demand requirements that the customers 84 arerequired to satisfy, expected order lead times for the customer'sindustry, or other features. These features may be identified using alead time history. As another example, product shipment size may be usedto categorize products, or channel efficiency may be used to categorizechannels.

[0049] A lead time profile for the supply chain 70 of a specificcustomer 84 is determined at step 106. The specific order lead timeprofile may be determined by identifying the category to which thespecific customer 84 belongs, and selecting the order lead time profilethat corresponds to the identified category from the order lead timeprofile options. According to one embodiment, the lead time profile fora specific customer 84 may be modified to customize the order lead timeprofile. As an example, the order lead time profile may be modified by auser using a user interface to account for a predicted change incustomer demand. The predicted change may result from, for example, itemshortages, profit increase, economic downturn, or other economic factor.As another example, the order lead time profile may be modified toaccount for a maximum offered lead time or a minimum offered lead time.An example order lead time profile is described in more detail withreference to FIG. 6.

[0050] Supply chain 70 is divided into order lead time segments (OLTSs)at step 110. An order lead time segment represents a portion of the pathof supply chain 70 that may be used to distribute order lead times anddemand upstream. Cycle times may be used to establish the order leadtime segments. A cycle time for a node 76 or arc 78 represents thedifference between the time when an item arrives at the node 76 or arc78 and the time when the item leaves the node 76 or arc 78. For example,the cycle time for a node 76 may include a manufacturing, production,processing, or other cycle time. The cycle time for an arc 78 mayinclude a distribution, transportation, or other cycle time. Acumulative cycle time for a node 76 represents the difference betweenthe time when an item arrives at the node 76 and the time when the endproduct is delivered to customer 84. A cumulative cycle time may includethe sum of one or more individual cycle times involved, for example, thecycle times for one or more nodes 76 and one or more arcs 78 involved.As an example, an order lead time segment may represent the differencebetween the cumulative cycle times for a first node 76 and an adjacentsecond node 76. Examples of order lead time segments are described withreference to FIG. 7.

[0051] The supply lead time (SLT) for each order lead time segment iscalculated at step 112. According to one embodiment, the supply leadtime SLT for an order lead time segment may be calculated according toSLT=μ+xσ for y % certainty. Values x and y may be determined accordingto standard confidence levels. For example, x=3 for y=99. According tothe example supply chain 70 of FIG. 4, for 99% certainty, the supplylead time for arc 78 c is 1.5+3(0.5)=3.0 days. Similarly, for 99%certainty, the supply lead time for arc 78 b is 2.0 days, and the supplylead time for arc 78 a is 3.0 days. The supply lead time, however, maybe calculated according to any suitable formula having any suitableparameters. For example, the supply lead time SLT may be calculatedaccording to SLT=p₁+p₂, where p₁ represents a minimum delay, and p₂represents an expected additional delay. Moreover, the supply lead timesmay have any suitable relationship with each other. For example, atleast two of the supply lead times may overlap. Furthermore, the supplylead times may be adjusted in any suitable manner. For example, a oneday padding may be added to one or more supply lead times.

[0052] Demand is redistributed to upstream order lead time segments atstep 114 in order to postpone inventory calculation to upstream nodes76. Demand may be redistributed by estimating demand percentages for theorder lead time segments. A demand percentage for an order lead timesegment represents the percentage of the demand that needs to besatisfied during the order lead time segment in order to satisfy thecustomer demand within the constraints of the order lead time profile.An example of calculating demand percentages is described with referenceto FIGS. 8 and 9.

[0053] Inventory that satisfies the demand percentages is established atnodes 76 at step 120. By calculating a demand percentage for each orderlead time segment, the inventory for the redistributed demand may bedetermined by postponing inventory calculation and individuallycalculating the inventory at each node 76. The inventory may bedetermined by calculating the inventory required at ending nodes 76 (forexample, nodes 76 d and 76 e) to satisfy the demand percentage of endingnodes 76. The calculated inventory generates a demand for a firstupstream node 76 (for example, node 76 c). The inventory at the firstupstream node 76 is determined to generate a demand for a secondupstream node 76 (for example, node 76 c), and so on. Inventory neededto satisfy the redistributed demand may be combined with inventoryneeded without regard to the redistributed demand in order to determinethe total demand needed at a node 76. A method for establishing theinventory is described in more detail with reference to FIGS. 10 through13.

[0054] Modifications, additions, or omissions may be made to the methodwithout departing from the scope of the invention. For example, orderlead time profiles need not be created for different categories at step104. Instead, an order lead time profile for the specific customer 84may simply be retrieved. Additionally, steps may be performed in anysuitable order without departing from the scope of the invention.

[0055]FIGS. 6A through 6C illustrate example order lead time profiles.An order lead time profile describes a demand corresponding to a node 76such as an ending node 76 (for example, node 76 d or 76 e). For example,an order lead time profile may describe demand associated with customer84 a of FIG. 4. The customer demand is placed on ending node 76 d tofulfill. In the illustrated embodiment, the order lead time profile isunconstrained (that is, assumes unlimited supply). Although the exampleorder lead time profiles are illustrated as graphs, the information ofthe order lead time profiles may be presented in any suitable manner,for example, in a table.

[0056]FIG. 6A illustrates an example order lead time profile. Accordingto the illustrated embodiment, a y axis 152 represents the cumulativepercentage of demand volume, and an x axis 154 represents the order leadtime expressed in days. According to one embodiment, a curve 160represents an example of an order lead time profile that describes thecumulative percentage of demand volume having a certain order lead time.Accordingly, a point (x, y) of curve 160 represents that cumulativepercentage y of the demand volume has an order lead time of x days. Forexample, a point P indicates that 33% of the demand volume has an orderlead demand time of less than 3 days, a point Q indicates that 90% ofthe demand volume has an order lead time of 30 days, and a point Rindicates that 100% of the demand volume has an order lead time of lessthan 60 days.

[0057] In one embodiment, order lead time profiles may be generated fordifferent group levels, for example, for all orders, all items, alllocations, or other group level. Generating order lead time profiles atthe group level may result in generating fewer profiles, which may beeasier to manage. Moreover, a user may be able to select a profile basedupon the group level of interest. In another embodiment, multiple orderlead time profiles may be generated for a group level. For example, anorder lead time profile may be generated for each item. Generatingmultiple order lead time profiles may allow for fine-tuned demandmonitoring. For example, where an order lead time profile is generatedfor each item, the order lead time profile for each item may beautomatically monitored for changes that may impact optimal inventorytarget levels.

[0058]FIGS. 6B and 6C illustrate example order lead time profilescustomized to account for maximum and minimum offered lead times,respectively. An order lead time profile may be customized using system10. Past performance is not necessarily a good indicator of futureperformance. System 10 gives the user an opportunity to override ormodify an order lead time profile using client system 10. An order leadtime profile may be customized to account for maximum and minimumoffered lead times. A user may want to impose a minimum offered leadtime on an order lead time profile. An order lead time profile may bemodified to reflect a minimum offered lead time by shifting the demandthat is less than the minimum offered lead time to the minimum offeredlead time. Moreover, a user may want to impose a maximum offered leadtime on an order lead time profile. An order lead time profile may bemodified to reflect a maximum offered lead time by shifting the demandthat is greater than the maximum offered lead time to the maximumoffered lead time.

[0059] In the illustrated example, curve 160 has been modified to takeinto account a minimum offered lead time and a maximum offered lead timeto yield curves 162 and 164, respectively. Curve 162 takes into accounta minimum offered lead time of 10 days, and curve 164 takes into accounta maximum offered lead time of 40 days. A curve 160 of an order leadtime profile may be modified in any other suitable manner to take intoaccount any other suitable feature. For example, order lead timeprofiles over time may be examined using a waterfall analysis todetermine trends. An order lead time profile may be adjusted to fit thetrends. As another example, an order lead time profile may be adjustedto provide a more conservative estimate or a less conservative estimate.

[0060]FIG. 7 is a bar graph 200 illustrating example cycle times fornodes 76 of supply chain 70. Bar graph 200 has a y axis that representsthe cumulative cycle time of a node 76, and an x axis that representsthe node 76. The cumulative cycle time represents the difference betweenthe time when an item reaches node 76 and the time when the end productis delivered to customer 84. According to bar graph 200, node 76 a has acumulative cycle time of 60 days, node 76 b has a cumulative cycle timeof 30 days, node 76 c has a cumulative time of 3 days, and nodes 76 dand 76 e each have a cumulative cycle time of 0 days.

[0061] The cumulative cycle times may be used to define order lead timesegments representing a difference between cumulative cycle times.According to one embodiment, an order lead time segment may representthe difference between cumulative cycle times for successive nodes 76.According to the illustrated embodiment, order lead time segment 1represents less than or equal to 3 days, order lead time segment 2represents greater than 3 and less than or equal to 30 days, order leadtime segment 3 represents greater than 30 and less than or equal to 60days, and order lead time segment 4 represents greater than 60 days.Order lead time segments may, however, be defined in any suitablemanner.

[0062]FIG. 8 is a table 220 with example demand percentages. A demandpercentage represents the percentage of the demand that needs to besatisfied during an order lead time segment in order to satisfy an orderlead time profile.

[0063] According to the illustrated example, table 220 illustrates howto calculate demand percentages for order lead time segments 1 through 4of FIG. 7 using order lead time profile curve 160 of FIG. 6. Table 220shows the range of each segment determined as described previously withreference to FIG. 7. The endpoints of each segment correspond to pointsof curve 160 of FIG. 6. For example, the three day endpoint correspondsto point P, the 30 day endpoint corresponds to point Q, and the 60 dayendpoint corresponds to point R.

[0064] Each point of curve 160 indicates a cumulative percentage of thedemand that corresponds to the number of days. For example, point Pindicates that 33% corresponds to 3 days, point Q indicates that 90%corresponds to 30 days, and point R indicates that 100% corresponds to60 days. The difference in the demand corresponding to the endpoints ofthe order lead time segment yields the demand percentage. Accordingly,order lead time segment 1 has a demand percentage of 33%−0%=33%, orderlead time segment 2 has a demand percentage of 90%−33%=57%, order leadtime segment 3 has a demand percentage of 100%−90%=10%, and order leadtime segment 4 has a demand difference of 100%−100%=0%.

[0065]FIG. 9 is a diagram illustrating an example redistributed demandfor an example supply chain 70. According to the illustrated example,the demand may be redistributed according to table 220 of FIG. 8. Thedemand percentage for OLTS1 is 33%, for OLTS2 is 57%, for OLTS3 is 10%,and for OLTS4 is 0%.

[0066]FIGS. 10 through 13 illustrate example procedures for calculatinginventory for the nodes 76 of a supply chain 70, given the demand,supply lead times, and customer service level for the nodes 76. If thedemand for a supply chain 70 is redistributed to upstream nodes 76, theinventory for the nodes 76 may be calculated for the distributed demand,which may be calculated using the demand percentages of the nodes 76.The inventory for the distributed demand may then be combined with theinventory for customer demand to obtain the total inventory for nodes76.

[0067]FIG. 10 illustrates an example supply chain portion 240 with anode 76 (node 1) for which an inventory may be calculated. According toone embodiment, the customer service level CSL for node 1 may beexpressed according to Equation (1):

CSL=1−EBO/μ _(d)  (1)

[0068] where EBO represents the expected back order of node 1 and μ_(d)represents the mean lead time demand. Expected back order representsinsufficient inventory of node 76 to meet demand at node 76. The leadtime demand describes the demand for a lead time segment. Expected backorder EBO may be calculated according to Equation (2): $\begin{matrix}{{E\quad B\quad O} = {\int_{s}^{\infty}{\left( {x - {f\quad s}} \right){p(x)}\quad {x}}}} & (2)\end{matrix}$

[0069] where p(x) represents the probability density function around themean lead time demand, s represents a reorder point, and f represents apartial fulfillment factor. If partial fills are not allowed, then f=0and the term drops out. The demand distribution may typically beconsidered a Normal distribution for relatively fast moving items interms of demand over lead time, a Gamma distribution for items moving ata relatively intermediate speed in terms of demand over lead time, or aPoisson distribution for relatively slow moving items in terms of demandover lead time. The distribution may be selected by a user or may be adefault selection. The mean lead time demand may be calculated accordingto Equation (3): $\begin{matrix}{\mu_{d} = {\int_{- \infty}^{\infty}{x\quad {p(x)}\quad {x}}}} & (3)\end{matrix}$

[0070] According to one example, for a fixed supply lead time (SLT), theinventory of node 1 may be calculated to propagate demand given the meanlead time demand μ_(d) of demand d, the standard deviation of lead timedemand σ_(d) of demand d (where standard deviation is used as oneexample measure of variability), and the customer service level CSL.According to the illustrated example, mean lead time demand μ_(d) is1000 units with a variability σ_(d) of 10 units, and node 1 has acustomer service level CSL of 96%. The inventory needed to cover meanlead time demand μ_(d) with x customer service level may be calculatedas μ_(d)+xσ_(d), where x corresponds to y according to standardconfidence levels. For example, node 1 needs μ_(d)+2σ_(d) to cover thedemand 96% of the time. In the illustrated example, the inventory neededat node 1 is μ_(d)+2σ_(d)=1020 units. To satisfy the remaining demand,there is an expected back order EBO=μ_(d)×(1-CSL). In the illustratedexample, the expected back order EBO =μ_(d)×(1-CSL)=40 units. Inventorymay be calculated for a number m of time periods by multiplying theinventory units by m.

[0071] According to one embodiment, demand may be propagated todetermine the mean lead time demand and variability at each node 76.Then, inventory may be calculated at individual nodes 76 using knowntechniques, which may simplify inventory optimization. In other words, acomplicated multi-echelon supply chain problem may be reduced to aseries of simpler single echelon supply chain problems.

[0072]FIG. 11 illustrates an example supply chain portion 250 thatincludes one node 76 (node 1) supplying another node 76 (node 2).According to the illustrated embodiment, node 1 has a demand d over thelead time with a demand variability of σ_(d). Node 1 has a customerservice level CSL1 and a supply lead time SLT1 with a supply lead timevariability of σ_(SLT1), and node 2 has a customer service level CSL2and a supply lead time SLT2 with a supply lead time variability ofσ_(SLT2).

[0073] According to one embodiment, the supply lead time for node 1 maybe calculated according to Equation (4):

CSL 2*SLT 1+(1-CSL 2)*(SLT 1+SLT 2)  (4)

[0074] and the supply lead time variability may be calculated accordingto Equation (5):

CSL 2*σ_(SLT1)+(1-CSL 2)*((σ_(SLT1)+σ_(SLT2))  (5)

[0075]FIG. 12 illustrates an example supply chain portion 270 thatincludes one node 76 (node 3) supplying two nodes 76 (nodes 1 and 2).Node 1 has a demand d1 with a demand variability of σ_(d1) and acustomer service level CSL1. Node 2 has a demand d2 with a demandvariability of σ_(d2) and a customer service level CSL2. Node 1 has asupply lead time SLT1 with a supply lead time variability σ_(SLT1), andnode 2 has a supply lead time SLT2 with a supply lead time variabilityσ_(SLT2). Node 3 has a supply lead time SLT3 with a supply lead timevariability of σ_(SLT3).

[0076] According to one embodiment, supply chain portion 270 representsa single distribution center that supports multiple distribution centersor a single die that makes multiple products. The demand at node 3 maybe given by d1+d2 with a demand variability given by Equation (6):

{square root}{square root over (σ_(d1) ²+σ_(d2) ^(2+cov(σ)_(d1),σ_(d2)))}  (6)

[0077] In a simple case, the covariance may be assumed to equal zero.The supply lead time and supply lead time variability of node 1 may becalculated according to Equations (4) and (5), respectively. Accordingto another embodiment, supply chain portion 270 may represent a node 76with multiple demand streams. According to this embodiment, supply chainportion 270 may represent multiple demand streams if supply lead timeSLT1=0, supply lead time variability σ_(SLT1)=0, supply lead timeSLT2=0, and supply lead time variable σ_(SLT2)=0. According to oneembodiment, demand of nodes 1 and 2 may be aggregated at node 3. Thedemand of nodes 1 and 2 may be pooled in order to calculate the demandof node 3.

[0078]FIG. 13 illustrates an example supply chain portion 280 thatincludes two nodes 76 (nodes 2 and 3) supplying one node 76 (node 1).Node 1 has a customer service level CSL1 and a demand d1 with a demandvariability σ_(d1). Node 2 has a customer service level CSL2 and node 3has a customer service level CSL3. Node 1 has a supply lead time SLT2with a supply lead time variability σ_(SLT2) from node 2, and a supplylead time SLT3 with a supply lead time variability σ_(SLT3) from node 3.

[0079] According to one embodiment, supply chain portion 280 mayrepresent product substitutions, alternative components, or alternatedistribution routes. According to the embodiment, supply chain portion280 represents node 1 receiving supplies from alternate sources nodes 2and 3. Node 1 receives a portion θ, where 0≦θ≦1, from node 2 and aportion 1-θ from node 3. According to this embodiment, the lead time fornode 1 may be given by Equation (7):

θ*SLT 1+(1-θ)*SLT 3  (7)

[0080] with a lead time variability given by Equation (8):

θ*σ_(SLT1)+(1-θ)*σ_(SLT2)  (8)

[0081] According to another embodiment, supply chain portion 280 mayrepresent node 1 requiring supplies from both nodes 2 and 3 to create orassemble a product. According to this embodiment, this representation ofportion θ is not used since node 1 requires items from both nodes 2 and3. According to the embodiment, the lead time at node 1 may be given byEquation (9):

Max(SLT2,SLT3)  (9)

[0082] with a lead time variability given by Equation (10):

⅓[Max(SLT 2+xσ_(SLT2) ,SLT 3+xσ_(SLT3))−Max(SLT 2,SLT 3)]  (10)

[0083] where x may be determined according to standard confidencelevels. For example, x=3 for a 99% confidence level.

[0084] To summarize, FIGS. 10 through 13 illustrate example proceduresfor calculating inventory for the nodes 76 of a supply chain 70. Theinventory may be calculated given the demand, supply lead times, andcustomer service level for the node 76. If the demand for a supply chain70 is redistributed to upstream node 76, the inventory for the nodes 76may be calculated for the redistributed demand, which may be calculatedusing the demand percentages of the nodes 76. Inventory needed tosatisfy the redistributed demand may be combined with inventory neededwithout regard to the redistributed demand in order to determine thetotal demand needed at a node 76.

[0085] Certain embodiments of the invention may provide one or moretechnical advantages. For example, demand may be redistributed from anending node to upstream nodes of a supply chain according to aprobability distribution for expected order lead time. Redistributingthe demand to upstream nodes may allow for optimizing inventory atindividual nodes, which may simplify the optimization. Inventory for thesupply chain may be optimized for the redistributed demand. Optimizinginventory for redistributed demand may decrease the need to stockinventory at downstream nodes, which may minimize cost. Inventory may beoptimized with respect to a probability distribution for expected orderlead time for a customer. Taking into account the order lead time mayimprove continued performance, which may lead to increased market share.

[0086] Although an embodiment of the invention and its advantages aredescribed in detail, a person skilled in the art could make variousalterations, additions, and omissions without departing from the spiritand scope of the present invention as defined by the appended claims.

what is claimed is:
 1. A method for optimizing inventory targets fornodes in a multi-echelon supply chain to satisfy a target customerservice level, comprising: accessing a supply chain model comprising anassumed value for each of the following inputs for a first time period:mean order lead time; variability of order lead time; for each of anumber of order lead time intervals, mean demand within the order leadtime interval; for each of the number of order lead time intervals,variability of demand within the order lead time interval; mean supplylead time for each of the nodes; and variability of supply lead time foreach of the nodes; for the first time period, according to the supplychain model including the assumed values for the inputs, calculating anoptimized inventory target for each of the nodes to satisfy the targetcustomer service level; for the first time period, accessing a measuredactual customer service level and a measured actual value for each ofthe inputs; if the measured actual customer service level for the firsttime period does not satisfy the target customer service level, then:for each of the inputs, determining a deviation between the measuredactual and assumed values for the input for the first time period; andidentifying at least one of the inputs for which the deviation for thefirst time period is significant to be a root cause of the measuredactual customer service level for the first time period not satisfyingthe target customer service level; and for a subsequent second timeperiod, using the determined deviation for the identified input for thefirst time period as feedback: adjusting the assumed value for theidentified input in the supply chain model; and calculating areoptimized inventory target for each of the nodes to satisfy the targetcustomer service level.
 2. The method of claim 1, wherein thevariability of order lead time, demand, and supply lead time comprisesthe standard deviation of order lead time, demand, and supply lead time,respectively.
 3. The method of claim 1, wherein calculating theoptimized inventory targets comprises: propagating a portion ofestimated demand on an end node in the supply chain to one or moreupstream nodes in the supply chain according to estimated order leadtime information; calculating the optimized inventory target for eachnode according to the portion of the estimated demand on the nodeindependently of the calculation of the optimized inventory target forevery other node, the optimized inventory target for the end node beingcalculated according to the portion of the estimated demand notpropagated to the one or more upstream nodes, the optimized inventorytarget for each of the one or more upstream nodes being calculatedaccording to the portion of the estimated demand propagated to theupstream node.
 4. The method of claim 3, wherein calculating theoptimized inventory targets further comprises independently calculatingthe optimized inventory target for each of a plurality of nodes using adifferent computer processor in a distributed processing environment. 5.The method of claim 1, wherein the deviations between the measuredactual and assumed values for the inputs are determined according todefined workflows that are consistent and repeatable over a plurality ofsuccessive time periods.
 6. The method of claim 1, further comprisingrepeating the steps of calculating optimized inventory targets tosatisfy the target customer service level, accessing a measured actualcustomer service level, if the measured actual customer service leveldoes not satisfy the target customer service level then determining adeviation between the measured actual and assumed values for each inputand identifying an input for which the deviation is significant as aroot cause, adjusting the assumed value for the identified input, andcalculating reoptimized inventory targets to satisfy the target customerservice level in an iterative closed-loop process that is consistent andrepeatable over a plurality of successive time periods, the iterativeclosed-loop process having the assumed values of the inputs as itsinputs and the measured actual customer service level as its output. 7.A system for optimizing inventory targets for nodes in a multi-echelonsupply chain to satisfy a target customer service level, comprising: adatabase operable to store a supply chain model; and a server systemcoupled to the database and operable to: access the supply chain modelcomprising an assumed value for each of the following inputs for a firsttime period: mean order lead time; variability of order lead time; foreach of a number of order lead time intervals, mean demand within theorder lead time interval; for each of the number of order lead timeintervals, variability of demand within the order lead time interval;mean supply lead time for each of the nodes; and variability of supplylead time for each of the nodes; for the first time period, according tothe supply chain model including the assumed values for the inputs,calculate an optimized inventory target for each of the nodes to satisfythe target customer service level; for the first time period, access ameasured actual customer service level and a measured actual value foreach of the inputs; if the measured actual customer service level forthe first time period does not satisfy the target customer servicelevel, then: for each of the inputs, determine a deviation between themeasured actual and assumed values for the input for the first timeperiod; and identify at least one of the inputs for which the deviationfor the first time period is significant to be a root cause of themeasured actual customer service level for the first time period notsatisfying the target customer service level; and for a subsequentsecond time period, using the determined deviation for the identifiedinput for the first time period as feedback: adjust the assumed valuefor the identified input in the supply chain model; and calculate areoptimized inventory target for each of the nodes to satisfy the targetcustomer service level.
 8. The system of claim 7, wherein thevariability of order lead time, demand, and supply lead time comprisesthe standard deviation of order lead time, demand, and supply lead time,respectively.
 9. The system of claim 7, wherein the server system isoperable to calculate the optimized inventory targets by: propagating aportion of estimated demand on an end node in the supply chain to one ormore upstream nodes in the supply chain according to estimated orderlead time information; calculating the optimized inventory target foreach node according to the portion of the estimated demand on the nodeindependently of the calculation of the optimized inventory target forevery other node, the optimized inventory target for the end node beingcalculated according to the portion of the estimated demand notpropagated to the one or more upstream nodes, the optimized inventorytarget for each of the one or more upstream nodes being calculatedaccording to the portion of the estimated demand propagated to theupstream node.
 10. The system of claim 9, wherein the server system isoperable to calculate the optimized inventory targets by independentlycalculating the optimized inventory target for each of a plurality ofnodes using a different computer processor in a distributed processingenvironment.
 11. The system of claim 7, wherein the deviations betweenthe measured actual and assumed values for the inputs are determinedaccording to defined workflows that are consistent and repeatable over aplurality of successive time periods.
 12. The system of claim 7, theserver system further operable to repeat the steps of calculatingoptimized inventory targets to satisfy the target customer servicelevel, accessing a measured customer service level, if the measuredactual customer service level does not satisfy the target customerservice level then determining a deviation between the measured actualand assumed values for each input and identifying an input for which thedeviation is significant as a root cause, adjusting the assumed valuefor the identified input, and calculating reoptimized inventory targetsto satisfy the target customer service level in an iterative closed-loopprocess that is consistent and repeatable over a plurality of successivetime periods, the iterative closed-loop process having the assumedvalues of the inputs as its inputs and the measured actual customerservice level as its output.
 13. Software for optimizing inventorytargets for nodes in a multi-echelon supply chain to satisfy a targetcustomer service level, the software embodied in a computer-readablemedium and when executed by a computer operable to: access a supplychain model comprising an assumed value for each of the following inputsfor a first time period: mean order lead time; variability of order leadtime; for each of a number of order lead time intervals, mean demandwithin the order lead time interval; for each of the number of orderlead time intervals, variability of demand within the order lead timeinterval; mean supply lead time for each of the nodes; and variabilityof supply lead time for each of the nodes; for the first time period,according to the supply chain model including the assumed values for theinputs, calculate an optimized inventory target for each of the nodes tosatisfy the target customer service level; for the first time period,access a measured actual customer service level and a measured actualvalue for each of the inputs; if the measured actual customer servicelevel for the first time period does not satisfy the target customerservice level, then: for each of the inputs, determine a deviationbetween the measured actual and assumed values for the input for thefirst time period; and identify at least one of the inputs for which thedeviation for the first time period is significant to be a root cause ofthe measured actual customer service level for the first time period notsatisfying the target customer service level; and for a subsequentsecond time period, using the determined deviation for the identifiedinput for the first time period as feedback: adjust the assumed valuefor the identified input in the supply chain model; and calculate areoptimized inventory target for each of the nodes to satisfy the targetcustomer service level.
 14. The software of claim 13, wherein thevariability of order lead time, demand, and supply lead time comprisesthe standard deviation of order lead time, demand, and supply lead time,respectively.
 15. The software of claim 13, operable to calculate theoptimized inventory targets by: propagating a portion of estimateddemand on an end node in the supply chain to one or more upstream nodesin the supply chain according to estimated order lead time information;calculating the optimized inventory target for each node according tothe portion of the estimated demand on the node independently of thecalculation of the optimized inventory target for every other node, theoptimized inventory target for the end node being calculated accordingto the portion of the estimated demand not propagated to the one or moreupstream nodes, the optimized inventory target for each of the one ormore upstream nodes being calculated according to the portion of theestimated demand propagated to the upstream node.
 16. The software ofclaim 15, operable to calculate the optimized inventory targets byindependently calculating the optimized inventory target for each of aplurality of nodes using a different computer processor in a distributedprocessing environment.
 17. The software of claim 13, wherein thedeviations between the measured actual and assumed values for the inputsare determined according to defined workflows that are consistent andrepeatable over a plurality of successive time periods.
 18. The softwareof claim 13, further operable to repeat the steps of calculatingoptimized inventory targets to satisfy the target customer servicelevel, accessing a measured actual customer service level, if themeasured actual customer service level does not satisfy the targetcustomer service level then determining a deviation between the measuredactual and assumed values for each input and identifying an input forwhich the deviation is significant as a root cause, adjusting theassumed value for the identified input, and calculating reoptimizedinventory targets to satisfy the target customer service level in aniterative closed-loop process that is consistent and repeatable over aplurality of successive time periods, the iterative closed-loop processhaving the assumed values of the inputs as its inputs and the measuredactual customer service level as its output.
 19. A system for optimizinginventory targets for nodes in a multi-echelon supply chain to satisfy atarget customer service level, comprising: means for accessing a supplychain model comprising an assumed value for each of the following inputsfor a first time period: mean order lead time; variability of order leadtime; for each of a number of order lead time intervals, mean demandwithin the order lead time interval; for each of the number of orderlead time intervals, variability of demand within the order lead timeinterval; mean supply lead time for each of the nodes; and variabilityof supply lead time for each of the nodes; for the first time period,according to the supply chain model including the assumed values for theinputs, means for calculating an optimized inventory target for each ofthe nodes to satisfy the target customer service level; for the firsttime period, means for accessing a measured actual customer servicelevel and a measured actual value for each of the inputs; if themeasured actual customer service level for the first time period doesnot satisfy the target customer service level, then: for each of theinputs, means for determining a deviation between the measured actualand assumed values for the input for the first time period; and meansfor identifying at least one of the inputs for which the deviation forthe first time period is significant to be a root cause of the measuredactual customer service level for the first time period not satisfyingthe target customer service level; and for a subsequent second timeperiod, using the determined deviation for the identified input for thefirst time period as feedback: means for adjusting the assumed value forthe identified input in the supply chain model; and means forcalculating a reoptimized inventory target for each of the nodes tosatisfy the target customer service level.
 20. A method for optimizinginventory targets for nodes in a multi-echelon supply chain to satisfy atarget customer service level, comprising: accessing a supply chainmodel comprising an assumed value for each of the following inputs for afirst time period: mean order lead time; variability of order lead time;for each of a number of order lead time intervals, mean demand withinthe order lead time interval; for each of the number of order lead timeintervals, variability of demand within the order lead time interval;mean supply lead time for each of the nodes; and variability of supplylead time for each of the nodes, the variability of order lead time,demand, and supply lead time comprising the standard deviation of orderlead time, demand, and supply lead time, respectively; for the firsttime period, according to the supply chain model including the assumedvalues for the inputs, calculating an optimized inventory target foreach of the nodes to satisfy the target customer service level by:propagating a portion of estimated demand on an end node in the supplychain to one or more upstream nodes in the supply chain according toestimated order lead time information; calculating the optimizedinventory target for each node according to the portion of the estimateddemand on the node independently of the calculation of the optimizedinventory target for every other node, the optimized inventory targetfor the end node being calculated according to the portion of theestimated demand not propagated to the one or more upstream nodes, theoptimized inventory target for each of the one or more upstream nodesbeing calculated according to the portion of the estimated demandpropagated to the upstream node, the optimized inventory target for eachof a plurality of nodes independently calculated using a differentcomputer processor in a distributed processing environment; for thefirst time period, accessing a measured actual customer service leveland a measured actual value for each of the inputs; if the measuredactual customer service level for the first time period does not satisfythe target customer service level, then: for each of the inputs,determining a deviation between the measured actual and assumed valuesfor the input for the first time period, the deviation between themeasured actual and assumed values for the inputs determined accordingto defined workflows that are consistent and repeatable over a pluralityof successive time periods; and identifying at least one of the inputsfor which the deviation for the first time period is significant to be aroot cause of the measured actual customer service level for the firsttime period not satisfying the target customer service level; for asubsequent second time period, using the determined deviation for theidentified input for the first time period as feedback: adjusting theassumed value for the identified input in the supply chain model; andcalculating a reoptimized inventory target for each of the nodes tosatisfy the target customer service level; and repeating the steps ofcalculating optimized inventory targets to satisfy the target customerservice level, accessing a measured actual customer service level, ifthe measured actual customer service level does not satisfy the targetcustomer service level then determining a deviation between the measuredactual and assumed values for each input and identifying an input forwhich the deviation is significant as a root cause, adjusting theassumed value for the identified input, and calculating reoptimizedinventory targets to satisfy the target customer service level in aniterative closed-loop process that is consistent and repeatable over aplurality of successive time periods, the iterative closed-loop processhaving the assumed values of the inputs as its inputs and the measuredactual customer service level as its output.